Software for numerical simulation of convection in spherical shells for hybrid CPU/GPU computing systems
Matematičeskoe modelirovanie, Tome 26 (2014) no. 10, pp. 95-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper describes the software developed by the authors for numerical 3D simulation of hydrodynamics and heat transfer in spherical shells. The software was developed using the OpenCL standard and is intended to run on hybrid CPU/GPU computing systems. The computing system was based on GPU Nvidia GTX Titan. The results of tests had demonstrated the accuracy of numerical solution and the efficiency of the usage of GPUs for solving problems of computational fluid dynamics.
Mots-clés : CFD
Keywords: spherical shell, GPU, OpenCL.
@article{MM_2014_26_10_a6,
     author = {I. V. Bychin and V. A. Galkin and T. V. Gavrilenko and A. V. Gorelikov and A. V. Ryakhovsky},
     title = {Software for numerical simulation of convection in spherical shells for hybrid {CPU/GPU} computing systems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {95--108},
     publisher = {mathdoc},
     volume = {26},
     number = {10},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_10_a6/}
}
TY  - JOUR
AU  - I. V. Bychin
AU  - V. A. Galkin
AU  - T. V. Gavrilenko
AU  - A. V. Gorelikov
AU  - A. V. Ryakhovsky
TI  - Software for numerical simulation of convection in spherical shells for hybrid CPU/GPU computing systems
JO  - Matematičeskoe modelirovanie
PY  - 2014
SP  - 95
EP  - 108
VL  - 26
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2014_26_10_a6/
LA  - ru
ID  - MM_2014_26_10_a6
ER  - 
%0 Journal Article
%A I. V. Bychin
%A V. A. Galkin
%A T. V. Gavrilenko
%A A. V. Gorelikov
%A A. V. Ryakhovsky
%T Software for numerical simulation of convection in spherical shells for hybrid CPU/GPU computing systems
%J Matematičeskoe modelirovanie
%D 2014
%P 95-108
%V 26
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2014_26_10_a6/
%G ru
%F MM_2014_26_10_a6
I. V. Bychin; V. A. Galkin; T. V. Gavrilenko; A. V. Gorelikov; A. V. Ryakhovsky. Software for numerical simulation of convection in spherical shells for hybrid CPU/GPU computing systems. Matematičeskoe modelirovanie, Tome 26 (2014) no. 10, pp. 95-108. http://geodesic.mathdoc.fr/item/MM_2014_26_10_a6/

[1] TOP-500. List of World's Supercomputers, (data obrascheniya 05.11.2013) http://www.top500.org/

[2] NVIDIA Tesla Kepler Family Datasheet, (data obrascheniya 05.11.2013) http://www.nvidia.ru/content/tesla/pdf/NVIDIA-Tesla-Kepler-Family-Datasheet.pdf

[3] Eksaflopsnye tekhnologii kontseptsii po razvitiyu tekhnologii vysokoproizvoditelnykh vychislenii na baze SUPEREVM eksaflopsnogo klassa (2012–2020 gg.), (data obrascheniya 11.11.2013) http://www.rosatom.ru/resources/b186cd804a8838d1a1dca5801c9b04ac/esk_tex.pdf

[4] Standart OpenCL, (data obrascheniya 10.11.2013) http://www.khronos.org/opencl

[5] Munshi A., OpenCL Programming Guide, Addison-Wesley Professional, 2011, 603 pp.

[6] Scarpino M., OpenCL in Action: How to Accelerate Graphics and Computations, Manning Publications Co., 2011, 456 pp.

[7] Glatzmaier G. A., Roberts P. H., “A three-dimensional self-consistent computer simulation of a geomagnetic field reversal”, Nature, 377 (1995), 203–209 | DOI

[8] Glatzmaier G. A., Roberts P. H., “A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle”, Phys. Earth Planet. Inter., 91:1–3 (1995), 63–75 | DOI

[9] Song X., Richards P. G., “Seismological evidence for differential rotation of the Earth's inner core”, Nature, 382 (1996), 221–224 | DOI

[10] Reshetnyak M. Yu., “Vraschenie vnutrennego yadra Zemli v modeli geodinamo”, DAN, 380:5 (2001), 15–19 | MR

[11] Miesch M. S., Elliott J. R., Toomre J., Clune T. L., Glatzmaier G. A., Gilman P. A., “Threedimensional spherical simulations of solarconvection. I: Differential rotation and pattern evolution achieved with laminar and turbulent states”, Astrophys. J., 532 (2000), 593–615 | DOI

[12] Kageyama A., Miyagoshi T., Sato T., “Formation of current coils in geodynamo simulations”, Nature, 454 (2008), 1106–1109 | DOI

[13] Glatzmaier G. A., Geodynamo simulations — How realistic are they?, Annu. Rev. Earth Planet. Sci., 30 (2002), 237–257 | DOI

[14] NVIDIA GeForce GTX TITAN, (data obrascheniya 15.11.2013) http://www.nvidia.ru/object/geforce-gtx-titan-ru.html

[15] Patankar S., Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Energoatomizdat, M., 1984, 152 pp.

[16] Issa R. I., “Solution on the implicitly discretised fluid flow equations by operator-splitting”, Journal of Computational Physics, 61 (1985), 40–65 | MR

[17] Issa R. I., Gosman A. D., Watkins A. P., “The Computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme”, Journal of Computational Physics, 62 (1986), 66–82 | DOI | MR | Zbl

[18] Gorelikov A. V., Ryakhovskii A. V., “Chislennoe modelirovanie estestvennoi konvektsii v sfericheskom sloe”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2008, no. 3, 77–84

[19] Gorelikov A. V., Ryakhovskii A. V., Fokin A. S., “Chislennoe issledovanie nekotorykh nestatsionarnykh rezhimov estestvennoi konvektsii vo vraschayuschemsya sfericheskom sloe”, Vychislitelnaya mekhanika sploshnykh sred, 5:2 (2012), 184–192

[20] Bychin I. V., Gorelikov A. V., Ryakhovskii A. V., “Testirovanie programmnogo kompleksa dlya chislennogo modelirovaniya teploobmena i techeniya zhidkosti v sfericheskikh sloyakh”, Vestnik kibernetiki, 2013, no. 12, 81–88

[21] Sakharnykh N. A., Berezin S. B., Paskonov V. M., “Modelirovanie techenii v akvatorii Belogo morya: primenenie massivno-parallelnoi arkhitektury GPU”, Zhurnal «Superkompyutery», 2011, no. 2(6), 51–55

[22] Biblioteka MAGMA, (data obrascheniya 17.11.2013) http://icl.utk.edu/magma

[23] Biblioteka cuBLAS, (data obrascheniya 17.11.2013) https://developer.nvidia.com/cuBLAS

[24] IntelR C++ Compiler XE 13.1 User and Reference Guides, (data obrascheniya 20.11.2013) http://software.intel.com/sites/products/documentation/doclib/iss/2013/compiler/cpp-lin

[25] Standartnyi interfeis bazovykh podprogramm lineinoi algebry BLAS, (data obrascheniya 17.11.2013) http://www.netlib.org/blas

[26] Christensen U. R. et al., “A numerical dynamo benchmark”, Physics of the Earth and Planetary Interiors, 128 (2001), 25–34 | DOI

[27] Busse F. H., “Convective flows in rapidly rotating spheres and their dynamo action”, Physics of Fluids, 14:4 (2002), 1301–1314 | DOI | MR